Resistivity minimum in Pd : Pr dilute alloys

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Resistivity minimum in Pd : Pr dilute alloys

P. Lethuillier

To cite this version:

P. Lethuillier. Resistivity minimum in Pd : Pr dilute alloys. Journal de Physique, 1978, 39 (12), pp.1349-1353. �10.1051/jphys:0197800390120134900�. �jpa-00208877�

RESISTIVITY MINIMUM IN Pd : Pr DILUTE ALLOYS

P. LETHUILLIER

Laboratoire Louis-Néel, C.N.R.S., 166X, 38042 Grenoble Cedex, ^France (Reçu ^{le 19 mai} 1978, révisé le 22 juillet 1978, accepté le 28 août 1978)

Résumé. ²⁰¹⁴ Nous avons mesuré la résistivité électrique ^de quelques alliages Pd1- xPrx (x ^{= 0,02}

et 0,03) ^entre 1,5 ^et 300 K. Des minima de résistivité ont été observés vers 20 K. En dessous de ces

minima, la résistivité électrique varie linéairement avec log10 ^{T mais avec un} changement ^de pente

vers 4 K. Dans des composés cubiques ^de praséodyme, ^un tel minimum résultant d’un effet du

champ cristallin peut ^{être observé} quand ^le triplet 03935 ^est le niveau fondamental. Cependant, l’accord

entre les valeurs calculées avec la formule de Hirst qui ^tient compte ^du champ cristallin et les résultats

expérimentaux ^est très mauvais. A titre de comparaison, ^{nous avons} mesuré la résistivité électrique

de composés dilués Pd : Sm et Pd : Tm et des composés ^définis PrPd3 ^et SmPd3 qui ^ne présentent

pas de minimum de résistivité. Nous avons également ^{mesuré la} susceptibilité magnétique ^du composé Pd0,98Pr0,02;

Abstract. ²⁰¹⁴ The electrical resistivity ^{of some} Pd1 _xPrx (x ^{= 0.02 and} 0.03) alloys ^{has been measur-}

ed between 1.5 and 300 K. Resistivity minima have been observed around 20 K. Below the minimum,

the resistivity ^varies linearly ^with log10 T but there is a slope change ^at about 4 K. In praseodymium

cubic compounds, ^{such a} resistivity ^minimum resulting ^{from a} crystal field effect may be observed when the 03935 triplet ^{is the} ground ^state. However, ^the agreement between the values calculated with Hirst’s formula, which takes into account the crystal field and the experimental ^values is very

bad. For comparison, ^we have measured the electrical resistivity of Pd : Sm and Pd : Tm dilute

compounds ^{which exhibit no} resistivity ^{minimum, in the same} way ^as PrPd3 ^and SmPd3. ^{We have}

also measured the magnetic susceptibility ^{of the} compound Pd0.98Pr0.02.

Classification ^’

Physics ^Abstracts

72.15E - 75.20H

072.15E201375.20H 75.30C - 76.30K

1. Introduction. ^- So far, ^{a Kondo} effect, ^{due to} the

praseodymium

ion has been observed in two

systems :

Zr 1 -xPrxB12 (X ~

O.OI) [1]

and La1-xPrxSn3

(0.1 x 1) [2, 3]. ^From the decrease of the _super-

conducting transition temperature, ^{Fisk and Mat-}

thias [1] ] deduce that cerium, ^as

impurity

ⁱⁿ ZrB12,

is non

magnetic.

^{This is also the case} for cerium in the definite

compound CeSn3

[4]. Thus, ^one may think that the occurrence of a Kondo

phenomenon

due to the

praseodymium

^{ion is favoured when the}

cerium ion,

placed

^{in the same matrix, is non} magnetic.

Susceptibility

measurements [5, 6] show that the cerium, ^as

impurity

^is

palladium,

^{is non}

magnetic

^and

no

resistivity

minimum is observed for this compound

between 1.5 and 25 K [6]. ^{In order to observe a Kondo} effect, ^a large density ^of states at the Fermi level is also favourable. For these _reasons, we have chosen

to study ^{the Pd : Pr dilute}

alloys.

2. Experiment. ^{- The}

purity

^{of the}

palladium

^and

of the

praseodymium

^were

respectively

^99.99

%

^and

99.9

%.

^The

Pd,.97X,.,3

(X ⁼ Pr, Sm, Tm)

alloys

have been melted on a water-cooled _copper

ftoating

boat with an induction

technique

^and very

rapidly quenched.

^The

compounds PdO.9sPrO.02, Pdo.98LUO.02, PrPd3

^and

SmPd3

have been melted in an induction furnace in alumina crucibles.

Samples

^of

approximate

dimensions 1.5 x 1.5 ^x 15 MM3 have been cut by spark ^erosion. X-ray measurements on the dilute Pd : X alloys ^{showed a f.c.c. structure with a} parameter close to the lattice constant of the

palladium.

The electrical

resistivity

measurements have been

performed

^{between 1.5 and 300 K}

by

^a classical A.C.

four

probe technique.

Electrical contacts were made

by very

sharp-pointed

^{brass screws.} The relative

precision

^{of the} measurements is 10-3 and the absolute

precision, including

the uncertainties

of sample

^dimen-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197800390120134900

1350

sions, ^{is about 2} %. ^{The error bars on the} temperature

are + 0.2 K.

We have also

performed

susceptibility ^measure-

ments on two compounds :

Pdo.98Pro.02

^and Pdo.98Lu0.02. ^The sensitivity of the translation balance is 10-9 e.m.u. and the relative

precision

^{of the measu-}

rements between two different compounds ^{of the}

same shape ^{is 10- 3.}

3. Resistivity measurements. ^-

Praseodymium

^is

soluble in

palladium

up ^{to a} concentration x ⁼ 0.02 [7].

The

compound Pdo.98Pro.02,

melted in an alumina crucible and cooled down

relatively’

slowly, ^was

found

by resistivity

^or

susceptibility

measurements to be homogeneous ^{within 12}

%.

^For

rapidly quenched alloys,

the limit of

solubility

^{of the}

praseodymium

reaches 4

%

[7]. ^The compound

Pdo.g,Pro.03,

^very

rapidly quenched,

^was

quite inhomogeneous

owing

to the large temperature

gradient during

^{the melt.}

Indeed, ^five samples ^{were cut in this} ingot ^{and showed}

very different resistivities

(Fig.

1).

FIG. 1. ^- Electrical resistivities versus temperature ^{of dilute} Pd0.97Pr0.03 samples ^{and of} palladium.

All these compounds ^{exhibit a}

resistivity

^mini-

mum

ranging

^{from 15 to 24 K}

(Figs.

^{1 and} 2) except the

sample

⁵

(Fig.

1) ^{which has a residual} resistivity

close to the

palladium

value and thus a very small Pr concentration.

The

resistivity

^{versus T at low} temperature ^{of all} these compounds ^varies

approximately

linearly (Figs. 1

and 2). ^{Plotted versus}

loglo

^T

(Fig.

3), ^{the diffe-}

rences Ap ⁼ p

(sample

i) ^- p (Pd), vary linearly

FIG. 2. ^- Electrical resistivity ^{of the} compound Pdo.ggPro.02

versus temperature. The insert is the low temperature ^{data on an} expanded ^scale.

FIG. 3. ^- Différences p (sample i ) ^- p (Pd) ^versus logl o ^{T. Note}

the scale changes.

versus loglo ^T but there is a slope change ^{at 4 K.}

This result is also valid for the

homogeneous PdO.98PrO.02 alloy.

For all these

compounds,

^after

subtraction of the

resistivity

^of

sample

5, the resisti-

vity

minimum is at about 25 K and the

depth

^{of the}

minimum is about 6

%.

Therefore,

sample

⁵ might

be considered to be the correct matrix

resistivity.

In this _case, when

plotting

Ao ^versus

loglo T,

^the

slope

change ^{at 4 K would be}

slightly

^increased.

By ^{contrast, the} compounds

Pdo.97Smo.o3

^and

Pdo.97 Tmo.o3,

^which have been

prepared

^{with the}

same technique ^{as the} Pdo.97Pro.o3 alloys, ^{do not}

exhibit _any resistivity ^minimum (Fig. 4) ^{in a similar}

way ^to

PrPd3

^and

SmPd3.

All these results show without

ambiguity

^{that the} resistivity ^{minimum of the Pd : Pr} alloys ^{is a}

genuine

property ^{of the} system.

FIG. 4. ^- Electrical resistivities of Pdo.97Smo.o3 ^and Pdo.97 TmO.03

versus temperature.

4. Discussion. ^- From the low temperature ^resis- tivity ^behaviour of the Pd : Pr dilute alloys, ^we may expect ^{that the} ground ^{state is the} rs

triplet

(or ^that it is

quite

^{close to} the lowest level). We have then tried to

explain

the observed resistivity ^minimum by ^a crytal ^{field effect. Indeed, in Pr cubic} compounds,

a resistivity minimum may be observed but only

when the T5 triplet ^{is the}

ground

^{state. The} tempe-

rature

dependent spin

^disorder resistivity ^{due to}

the

scattering

^{of the} conduction electrons by ^the

crystal

^field levels has been calculated by ^Hirst [8].

It can be written

where the trace is taken over the 2 J + 1 crysta! ^field states 1 i > ^whose energies ^are Ei. The matrices P and Q eX ^{are :}

and

where kB ^{is the Boltzmann constant and} Pex is a

constant which

depends

^{on the} 4f-conduction electron interaction strength.

We have then

attempted

^to

explain

^{the low} tempe-

rature

resistivity

curves, trying ^a

large

^{number of} crystalline electric field (CEF) parameters ^{with the} T5

triplet

^as ground ^{state. The} agreement ^between calculated (Fig. 5) ^and experimental values is very

FIG. 5. ^- Reduced spin ^disorder resistivity ^versus temperature, calculated using ^{Hirst’s formula for a Pr3 + ion in a cubic} symmetry site with different values of the CEF parameters W ^{and x. The} dashed curve corresponds ^{to CEF} parameters ^which might explain

a possible Kondo effect and which ^are consistent with the Pd : Er CEF parameters [11].

poor. As there is a large density ^{of d} states at the Fermi level, ^{it is}

probably

necessary ^to take into account aspherical ^Coulomb scattering [9, 10] ^as suggested by Guertin et al.

[6].

^{It is then useful to}

determine the CEF parameters. ^{In the dilute Pd : Er} alloys, ^these parameters have been obtained by

Murani et al. [11] by ^neutron spectroscopy. They

have found,

using

^the classical notations of Lea et al. [12]. ^{W = - 0.17 K and x = 0.47, with}

and

W(l - 1 x 1)

⁼ A6

Y r6 >

F6. ^{If we suppose}

that A4 ^and A6 ^{are constant for all Pd : R dilute}

rare earth alloys, ^{we find for the Pd : Pr} alloys,

using

the rn > values calculated by ^{Freeman and Wat-}

son [13] ^{W = - 4.3 K and x = - 0.78. With these}

CEF parameters, ^the

ground

^{state is the} T5

triplet,

in agreement ^{with the} resistivity measurements.

With the close values,

1352

it is possible ^to explain

qualitatively

^{the curves}

of figure ^{3 in terms of a} Kondo effect. In fact, ^between

1.5 and 4 K the

spin

^disorder resistivity, ^calculated

with these parameters, ^increases rapidly (see ^the

dashed curve of figure 5) and then there is a plateau,

which might explain ^the

slope change

at 4 K of the

resistivity

^{curves of}

figure

^{3. Above 15} K, ^{the resis-} tivity ^increases

again rapidly

^which might ^{lead to}

the observed resistivity minima, ^the

decreasing loga-

rithmic

resistivity

^term

being

compensated by ^the

increase of the

spin

^disorder

resistivity.

^{Of course,}

these values of W and x would be only

approximate.

We may then remark that, with these CEF _para- meters, the

ground

^state is the doublet r 3, ^the

triplet

r 5

being

situated 0.2 K

higher.

However, our measure-

ments, made above 1.5 K, ^cannot

give

evidence of this fact.

Finally,

deviations from Matthiessen’s rule [14]

might

^also

give

^a contribution to the anomalous low temperature variation of the

resistivity

^{of the}

Pd : Pr dilute

alloys.

In order to understand these results better, ^we performed

susceptibility

measurements.

5. Susceptibüity measurements. ^- The magnetic

susceptibility

^{of two}

Pdo.98Pro.02

samples (1 ^and 2),

cut in the same

ingot,

has been measured between 4 and 300 K. At 4 K, ^the

susceptibility

^{of the} sample ¹

slightly

exceeds that of

sample

²

(by

¹²

%)

(Fig. 6),

FIG. 6. ^- Reciprocal susceptibilities ^{of two} compounds PdO.9sPrO.02

versus temperature after correction for the PdO.98Luo.02 ^matrix susceptibility.

indicating

^{that the Pr} concentration of these two

samples

^differs by ^about

12 % :

^{indeed at this} tempe- rature, the matrix

susceptibility

^{is weak} (about 13 %

of the Pr

susceptibility).

^{At room} temperature, ^the susceptibility ^{of our}

palladium

^{is :}

Quite clearly, ^{it is not} correct to subtract the _suscep-

tibility ^{of the}

palladium

^{so as to obtain the Pr contri-}

bution since this would lead, ^{at room} temperature,

to XPr ~ 10- 3 e.m.u. jMole ^or smaller values whereas

one should find _{XPr ~ 5} x 10-3 e.m.u./Mole. ^The

best matrix contribution to subtract would be the

susceptibility

^{of a}

Pdo.98Lao.o2 compound.

However, lanthanum is soluble in

palladium

only ^{when the}

alloy

is cooled _very

rapidly

[7]. ^{In this} case, the alloy

will be as

inhomogeneous

^{as our}

Pdo.gyPro 03

^com-

pound.

^{It is then,} necessary ^to consider that the correct matrix is

Pdo,9sLuo,o2,

^{as was used} by ^Shaltiel

et al. [5]. ^{For this}

compound,

^our measurements are

in agreement with those of Guertin et al.

[6].

^The

corrected

reciprocal susceptibilities

^{are shown in}

figure

^6. We may ^{now comment} that sample 2, which has a smaller Pr concentration than

sample

1, has a larger

susceptibility

^{at room} temperature.

This is _easy to

explain :

^{if we} consider that the Pr concentration of

sample

^{1 is}

exactly

²

%,

^{then that}

of

sample

^{2 will} be about 1.8

%

^so that the matrix

susceptibility

^to subtract will be that

ofPdo.982Luo.oi8-

At room temperature, this variation of the matrix contribution with the Lu concentration _may be estimated from the work of Guertin et al. [6] ^{to be}

2 ^x 10-5

e.m.u./Mole,

^{the Pd : Lu}

susceptibility decreasing

^{when the Lu} concentration increases.

Thus, ^{for the}

sample

2, ^a larger ^matrix

susceptibility

should be subtracted.

After correction for the matrix contribution the low temperature ^{Curie constants are}

respectively

1.35 and 1.4, whereas the theoretical Curie constant of Pr3 + is 1.6. This shows that the T5

triplet

^{is the}

ground

^state (or that it is

quite

^{close to the} ground state). ^The

high

temperature ^{Curie constant of the}

two

samples,

measured between 100 and 200 K is C ⁼ 2.5,

showing

^{that the Pr} concentration of our

samples

^is

slightly larger

^{than 2}

%.

Indeed, ^{in this} temperature

region,

since the matrix

susceptibility

has the same order of

magnitude

^{as the} Pr suscep-

tibility,

^{a small}

change

^{in the Pr} concentration will lead to a large variation of the Curie constant. With the parameters ^{which may}

explain

^a

possible

^Kondo

effect : W = - 4.3 K, ^{x = - 0.736} 5, ^{the low} temperature calculated Curie constant is C ~ 1.2,

in

good

agreement ^{with the}

experimental

^values

since the Pr concentration of our

samples slightly

exceeds 2

%.

6. Conclusion. ^- At present, ^{it is not}

possible

^to

say if the

resistivity

minimum observed in the

Pd1-xPrx compounds

arises from a Kondo effect or from a

crystal

field effect

including aspherical

^Coulomb

scattering. ^{For these}

compounds, susceptibility

^measu-

rements

give

^rather poor indications about the

crystal field level scheme and neutron spectroscopy would not

probably

be efficient

owing

^{to the small}

Pr moment and the weak Pr concentration. Low temperature

resistivity

measurements might ^{lead to}

the correct interpretation.

Acknowledgments. ^{- The} apparatus used for the

experiments

^{has been} constructed in collaboration with J. C. Genna. We thank him for his technical assistance and R. Perrier de la Bâthie for

helpful

discussions about metallurgy.

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